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Special Education – Instructional Math

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

HSA.REI.A.2

Math 1.1

I can interpret parts of an expression, such as terms, factors, and coefficients

HSA.SSE.1a

Math 1.2

I can explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

HSA.REI.1

Math 1.3

I can solve linear equations and inequalities in one variable, including equations with coefficients represented by letters

HSA.REI.3

Academic Vocabulary

Variable, coefficient, inverse, operation

Solve and Graph Linear Equations

Unit OutcomeMath 2

Graph linear and quadratic functions and show intercepts, maxima, and minima

HSF.IF.7a

Math 2.1

I can create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales

HSA.CED.2

Math 2.2

I can represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

HSA.CED.3

Math 2.3

I can calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

HSF.IF.6

Academic Vocabulary

Write and Interpret Linear Equations

Unit OutcomeMath 3

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions

HSA.CED.1

Math 3.1

I can distinguish between situations that can be modeled with linear functions and with exponential functions.b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

HSF.LE.1

Math 3.2

I can interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data

HSS.ID.7

Math 3.3

I can know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

HSA.CO.A.1

Academic Vocabulary

Write and Interpret Linear Inequalities

Unit OutcomeMath 4

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters

HSA.REI.3

Math 4.1

I can solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

HSA.REI B.3

Math 4.2

I can create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions

HSA.CED.1

Math 4.3

I can represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context

HSA.CED A.3

Academic Vocabulary

Solve Systems of Equations

Unit OutcomeMath 5

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

HSA.REI.5

Math 5.1

I can solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

HSA.REI.6

Math 5.2

I can understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

HSA. REI.D.10

Math 5.3

I can solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

HSA.REI.C.7

Academic Vocabulary

Simplify and Solve With Exponents

Unit OutcomeMath 6

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

HSA.RN.A.2

Math 6.1

I can explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

HSA.RN.B.3

Math 6.2

I can use the properties of exponents to interpret expressions for exponential functions.

HSA.IF.C.8.b

Math 6.3

I can explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents

HSA.RN.A.1

Academic Vocabulary

Simplify and Factor Polynomials

Unit OutcomeMath 7

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

HSA.APR.A.1

Math 7.1

I can know and apply the Remainder Theorem: For a polynomial
p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

HSA.APR.B.2

Math 7.2

I can identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

HSA.APR.B.3

Math 7.3

I can use the structure of an expression to identify ways to rewrite it.
For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).

HSA.SSE.A.2

Academic Vocabulary

Combine Fractions Using Mathematical Operations

Unit OutcomeMath 8

Interpret expressions that represent a quantity in terms of its context

HSA.SSE.A.1

Math 8.1

I can choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (reduce fractions)

HSA.SSE.B.3

Math 8.2

I can explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (combine fractions)

HSA.REI.A.1

Math 8.3

I can solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. (combine fractions)

HSA.REI.A.2

Academic Vocabulary

Use Geometric Formulas to Determine Area, Perimeter, and Volume

Unit OutcomeMath 9

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

HSG.GPE.B.7

Math 9.1

I can interpret expressions that represent a quantity in terms of its context (perimeter)

HSA.SSE.A.1

Math 9.2

I can use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. (area)

HSN.Q.A.1

Math 9.3

I can use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.(volume)

Perform life and daily tasks and interact with others in a positive manner

FLS 3.1

I can adapt communication to a variety of contexts and tasks using complete sentences when indicated or appropriate

EE.SL.11-12.6

FLS3.2

I can use general academic and domain-specific words and phrases across contexts. (EdMark Functional Word Series, food ingredients, cooking utensils, ect.)

EE.L.11-12.6.

FLS 3.3

I can determine the credibility and accuracy of information presented across diverse media or formats. (News, social media, social safety, social boundaries, human sexuality safety).

EE.SL.11-12.2.

FLS 3.4

I can use language to achieve desired outcomes when communicating. (a) Vary syntax when writing and communicating. (Phone skills, texting skills, appropriate language within different social groups/environments)

EE.L.9-10.3.

FLS3.5

I can engage in collaborative discussions. (a) Prepare for discussions by collecting information on the topic. (b) Work with adults and peers to set rules for discussions. (c) Relate the topic of discussion to broader themes or ideas. (d) Indicate agreement or disagreement with others during discussions.